This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

Can you make five differently sized squares from the tangram pieces?

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

Can you split each of the shapes below in half so that the two parts are exactly the same?

Surprise your friends with this magic square trick.

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

These pictures show squares split into halves. Can you find other ways?

Make a flower design using the same shape made out of different sizes of paper.

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Follow these instructions to make a three-piece and/or seven-piece tangram.

What shape is made when you fold using this crease pattern? Can you make a ring design?

Make a mobius band and investigate its properties.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

Follow these instructions to make a five-pointed snowflake from a square of paper.

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

An activity making various patterns with 2 x 1 rectangular tiles.

Did you know mazes tell stories? Find out more about mazes and make one of your own.

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

What do these two triangles have in common? How are they related?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

How can you make a curve from straight strips of paper?

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

Explore the triangles that can be made with seven sticks of the same length.

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Here are some ideas to try in the classroom for using counters to investigate number patterns.

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?